Finite Group Databasebeta

← #618461

Subgroups — #618461

Order 512.

4080 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#529C211yesmaximal, characteristic
2C2×#2487C211yesmaximal, characteristic, complemented
3C2×#2486C211yesmaximal, characteristic, complemented
4C2×#2317C211yesmaximal, characteristic, complemented
5#16024C212yesmaximal, complemented
6#15982C212yesmaximal, complemented
7#15950C212yesmaximal
8#15928C212yesmaximal, complemented
9#15881C212yesmaximal, complemented
10#15669C212yesmaximal, complemented
11#15430C212yesmaximal, complemented
12#15262C212yesmaximal, complemented
13#15181C212yesmaximal, complemented
14#15158C212yesmaximal, complemented
15#14697C212yesmaximal, complemented
16#14343C211yesmaximal, characteristic, complemented
17#14264C212yesmaximal, complemented
18#13871C211yesmaximal, characteristic, complemented
19#13871C211yesmaximal, characteristic, complemented
20C2×#529—28no—
21C2×#529—28no—
22C2×#529—28no—
23C22×#126C2211yescharacteristic
24C22×#126C2211yescharacteristic
25C22×#125C2211yescharacteristic
26C22×#124C2211yescharacteristic
27C22×#123C2211yescharacteristic
28C22×#123C2211yescharacteristic
29C22×#123C2212yes—
30C22×C22⋊Q8C2211yescharacteristic
31C22×#121C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35C22×C4×D4C2211yescharacteristic
36C22×#117C2211yescharacteristic
37C22×#117C2211yescharacteristic
38C22×#117C2211yescharacteristic
39C23×C4⋊C4C2211yescharacteristic
40C23×C42C2211yescharacteristic
41#2487—28no—
42#2486—28no—
43C2×#400C2212yes—
44C2×#399C2212yes—
45C2×#398C2212yes—
46C2×#397C2212yes—
47C2×#395C2214yes—
48#2317—28no—
49C2×#389C2212yes—
50C2×#389C2212yes—
51C2×#389C2212yes—
52C2×#389C2212yes—
53C2×#386C2212yes—
54C2×#385C2212yes—
55C2×#385C2212yes—
56C2×#385C2212yes—
57C2×#385C2214yes—
58C2×#384C2212yes—
59C2×#382C2212yes—
60C2×#381C2212yes—
61C2×#380C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×#380C2212yes—
64C2×#380C2212yes—
65C2×#380C2212yes—
66C2×#380C2212yes—
67#1445C2212yes—
68#1445C2212yes—
69#1444C2214yes—
70#1442C2214yes—
71#1442C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1440C2212yes—
76#1440C2212yes—
77#1440C2212yes—
78#1440C2212yes—
79#1439C2214yes—
80#1439C2214yes—
81#1439C2214yes—
82#1439C2214yes—
83#1438C2212yes—
84#1438C2212yes—
85#1438C2214yes—
86#1437C2212yes—
87#1437C2212yes—
88#1436C2212yes—
89#1436C2212yes—
90#1436C2214yes—
91#1436C2214yes—
92C4⋊#95C2212yes—
93C4⋊#95C2212yes—
94C4⋊#95C2212yes—
95C4⋊#95C2212yes—
96C22⋊#95C2214yes—
97C23×Q8C2311yescharacteristic
98C23×D4C2311yescharacteristic
99C23×D4C2311yescharacteristic
100C23×D4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2312yes—
107#529—2128no—
108C2×#126—24no—
109C2×#126—24no—
110C2×#126—24no—
111C2×#126—24no—
112C2×#126—24no—
113C2×#126—24no—
114C2×#125—24no—
115C2×#125—24no—
116C2×#125—24no—
117C2×#124—24no—
118C2×#124—24no—
119C2×#124—24no—
120C2×#123—24no—
121C2×#123—28no—
122C2×#123—24no—
123C2×#123—24no—
124C2×#123—24no—
125C2×#123—24no—
126C2×#123—24no—
127C2×#123—48no—
128C2×C22⋊Q8—24no—
129C2×C22⋊Q8—24no—
130C2×C22⋊Q8—24no—
131C2×#121—24no—
132C2×#121—24no—
133C2×#121—24no—
134C2×C4×Q8—24no—
135C2×C4×Q8—24no—
136C2×C4×Q8—24no—
137C2×C4×D4—24no—
138C2×C4×D4—24no—
139C2×C4×D4—24no—
140C2×C4×D4—24no—
141C2×C4×D4—24no—
142C2×C4×D4—24no—
143C2×C4×D4—24no—
144C2×C4×D4D418yes—
145C2×C4×D4D418yes—
146C2×#117—24no—
147C2×#117—24no—
148C2×#117—24no—
149C2×#117—24no—
150C2×#117—28no—
151C2×#117—24no—
152C2×#117—24no—
153C2×#117D418yes—
154C22×C4⋊C4—24no—
155C22×C4⋊C4—24no—
156C22×C4⋊C4—24no—
157C22×C4⋊C4C2314yes—
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2314yes—
174C22×C4⋊C4C2314yes—
175C22×C4⋊C4C2314yes—
176C22×C22⋊C4C2311yescharacteristic
177C22×C22⋊C4C2311yescharacteristic
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2311yescharacteristic
180C22×C22⋊C4C2311yescharacteristic
181C22×C22⋊C4C2314yes—
182C22×C22⋊C4C2311yescharacteristic
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2314yes—
189C22×C22⋊C4C2314yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2314yes—
192C22×C22⋊C4C2312yes—
193C22×C42—24no—
194C22×C42—24no—
195C22×C42—24no—
196C22×C42C2311yescharacteristic
197C22×C42C2311yescharacteristic
198C22×C42C2312yes—
199C22×C42C2311yescharacteristic
200C22×C42C2311yescharacteristic
201C22×C42C2311yescharacteristic
202C22×C42C2311yescharacteristic
203#400—28no—
204#399—28no—
205#398—28no—
206#397—28no—
207#395—48no—
208#389—28no—
209#389—28no—
210#389—28no—
211#389—28no—
212#386—28no—
213#385—28no—
214#385—28no—
215#385—28no—
216#385—48no—
217#384—28no—
218#382—28no—
219#381—28no—
220#380—28no—
221#380—24no—
222#380—28no—
223#380—24no—
224#380—28no—
225#380—28no—
226C2×#95C2314yes—
227C2×#95C2312yes—
228C2×#95C2314yes—
229C2×#95C2314yes—
230C2×#95C2312yes—
231C2×#95C2314yes—
232C2×#95C2314yes—
233C2×#95C2314yes—
234C2×#95C2314yes—
235C2×#95C2314yes—
236C2×#95C2314yes—
237C2×#95C2314yes—
238C2×#95C2314yes—
239C2×#95C2314yes—
240C2×#95C2314yes—
241C2×#95C2314yes—
242C2×#95C2314yes—
243C2×#95C2314yes—
244C25C2411yescharacteristic
245C25C2411yescharacteristic
246C25C2411yescharacteristic
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—24no—
251C22×Q8—42no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—24no—
259C22×D4—24no—
260C22×D4—22no—
261C22×D4—24no—
262C22×D4—42no—
263C22×D4—42no—
264C22×D4—42no—
265C22×D4C2×D414yes—
266C22×D4C2×D414yes—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—24no—
284C23×C4—24no—
285C23×C4—24no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—44no—
291C23×C4—44no—
292C23×C4C2×D414yes—
293C23×C4C2×D414yes—
294C23×C4C2×D414yes—
295C23×C4C2×D414yes—
296C23×C4C2×D414yes—
297C23×C4C2414yes—
298C23×C4C2414yes—
299C23×C4C2414yes—
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C23×C4C2414yes—
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313#126—232no—
314#126—232no—
315#125—232no—
316#124—232no—
317#123—232no—
318#123—232no—
319#123—432no—
320C22⋊Q8—232no—
321#121—232no—
322C4×Q8—232no—
323C4×D4—232no—
324C4×D4—232no—
325C4×D4—232no—
326#117—232no—
327#117—232no—
328#117—232no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—28no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—28no—
369C2×C4⋊C4—28no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—28no—
373C2×C4⋊C4—28no—
374C2×C4⋊C4—28no—
375C2×C4⋊C4—416no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4—44no—
378C2×C4⋊C4—44no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4—44no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4C2×D414yes—
383C2×C4⋊C4C2×D414yes—
384C2×C4⋊C4C2×D414yes—
385C2×C4⋊C4C2×D414yes—
386C2×C4⋊C4#4118yes—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—28no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—28no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—28no—
417C2×C22⋊C4—28no—
418C2×C22⋊C4—28no—
419C2×C22⋊C4—28no—
420C2×C22⋊C4—44no—
421C2×C22⋊C4—44no—
422C2×C22⋊C4—44no—
423C2×C22⋊C4—44no—
424C2×C22⋊C4—44no—
425C2×C22⋊C4—44no—
426C2×C22⋊C4—44no—
427C2×C22⋊C4—44no—
428C2×C22⋊C4—44no—
429C2×C22⋊C4C2×D414yes—
430C2×C22⋊C4C2×D414yes—
431C2×C22⋊C4C2×D414yes—
432C2×C22⋊C4C2×D414yes—
433C2×C22⋊C4C2×D414yes—
434C2×C22⋊C4C2×D414yes—
435C2×C42—232no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—24no—
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—22no—
451C2×C42—28no—
452C2×C42C2×D414yes—
453C2×C42C2×D414yes—
454C2×C42C2×D414yes—
455C2×C42C2×D414yes—
456#95—28no—
457#95—28no—
458#95—24no—
459#95—24no—
460#95—28no—
461#95—28no—
462#95—28no—
463#95—28no—
464#95—28no—
465#95—28no—
466#95—28no—
467#95—44no—
468#95—44no—
469#95—44no—
470#95—44no—
471#95—44no—
472#95—44no—
473#95—44no—
474C24—21no—
475C24—21no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—21no—
488C24—21no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24C22×D412yes—
496C24C22×D412yes—
497C24C22×D412yes—
498C24C22×D412yes—
499C24C22×D412yes—
500C242−1+414yes—
501C24C2511yescharacteristic
502C2×Q8—28no—
503C2×Q8—48no—
504C2×Q8—48no—
505C2×Q8—44no—
506C2×Q8—44no—
507C2×D4—28no—
508C2×D4—28no—
509C2×D4—28no—
510C2×D4—28no—
511C2×D4—28no—
512C2×D4—44no—
513C2×D4—44no—
514C2×D4—48no—
515C2×D4—48no—
516C2×D4—48no—
517C2×D4—48no—
518C2×D4—48no—
519C2×D4—48no—
520C2×D4—44no—
521C2×D4—44no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—28no—
528C22×C4—28no—
529C22×C4—216no—
530C22×C4—216no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—24no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—28no—
576C22×C4—28no—
577C22×C4—216no—
578C22×C4—216no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—88no—
618C22×C4—88no—
619C22×C4#120116yes—
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C22×D412yes—
623C22×C4C22×D412yes—
624C22×C4C22×D412yes—
625C22×C4C22×D412yes—
626C22×C4C22×D412yes—
627C22×C4C22×D412yes—
628C22×C4C22×D412yes—
629C22×C4C22×D412yes—
630C22×C4C22×D412yes—
631C22×C4C22×D412yes—
632C22×C4C22×D412yes—
633C22×C4C22×D412yes—
634C22×C4C22×D412yes—
635C22×C4C22×D412yes—
636C22×C4C2×#4118yes—
637C22×C4C2×#4114yes—
638C22×C4H(5,𝔽2)14yes—
639C22×C42−1+414yes—
640C4⋊C4—28no—
641C4⋊C4—28no—
642C4⋊C4—28no—
643C4⋊C4—28no—
644C4⋊C4—28no—
645C4⋊C4—28no—
646C4⋊C4—28no—
647C4⋊C4—28no—
648C4⋊C4—28no—
649C4⋊C4—28no—
650C4⋊C4—216no—
651C4⋊C4—48no—
652C4⋊C4—48no—
653C4⋊C4—416no—
654C4⋊C4—48no—
655C4⋊C4—48no—
656C4⋊C4—88no—
657C4⋊C4—88no—
658C4⋊C4—88no—
659C22⋊C4—216no—
660C22⋊C4—28no—
661C22⋊C4—28no—
662C22⋊C4—28no—
663C22⋊C4—28no—
664C22⋊C4—28no—
665C22⋊C4—28no—
666C22⋊C4—28no—
667C22⋊C4—28no—
668C22⋊C4—28no—
669C22⋊C4—28no—
670C22⋊C4—416no—
671C22⋊C4—48no—
672C22⋊C4—48no—
673C22⋊C4—416no—
674C22⋊C4—88no—
675C22⋊C4—88no—
676C42—28no—
677C42—28no—
678C42—216no—
679C42—28no—
680C42—28no—
681C42—28no—
682C42—28no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—24no—
695C23—24no—
696C23—24no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—24no—
701C23—24no—
702C23—24no—
703C23—24no—
704C23—24no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—24no—
709C23—24no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23C2×#12014yes—
745C23#53614yes—
746C23C23×D411yescharacteristic
747C23C23×D411yescharacteristic
748C23C23×D411yescharacteristic
749C23C22×#4112yes—
750C23C2×H(5,𝔽2)12yes—
751C23C2×2−1+412yes—
752C23C2×2−1+412yes—
753C23#58512yes—
754C23#58512yes—
755Q8—416no—
756D4—416no—
757D4—416no—
758D4—416no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—232no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—28no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—28no—
789C2×C4—28no—
790C2×C4—416no—
791C2×C4—416no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—44no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—44no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—416no—
823C2×C4—416no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—44no—
834C2×C4—44no—
835C2×C4—44no—
836C2×C4—44no—
837C2×C4—44no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—44no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—816no—
846C2×C4C2×#12014yes—
847C2×C4C2×#12014yes—
848C2×C4#52514yes—
849C2×C4#53514yes—
850C2×C4#53614yes—
851C2×C4#54718yes—
852C2×C4#54718yes—
853C22—28no—
854C22—24no—
855C22—24no—
856C22—24no—
857C22—24no—
858C22—44no—
859C22—44no—
860C22—44no—
861C22—44no—
862C22—44no—
863C22—44no—
864C22—44no—
865C22—44no—
866C22—44no—
867C22—42no—
868C22—42no—
869C22—44no—
870C22—44no—
871C22—44no—
872C22—44no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—82no—
877C22—82no—
878C22—82no—
879C22—82no—
880C22C22×#12011yescharacteristic
881C22C2×#52511yescharacteristic
882C22C2×#53511yescharacteristic
883C22C2×#53611yescharacteristic
884C22C2×#53611yescharacteristic
885C22#344911yescharacteristic
886C22#344911yescharacteristic
887C22C2×#54712yes—
888C22C2×#54712yes—
889C22#348812yes—
890C22#348812yes—
891C22#348912yes—
892C22#348912yes—
893C22#351612yes—
894C22#351712yes—
895C22#352012yes—
896C22#352112yes—
897C22#354712yes—
898C22#355212yes—
899C22#356312yes—
900C22#356512yes—
901C4—24no—
902C4—24no—
903C4—42no—
904C4—42no—
905C4—42no—
906C4—42no—
907C4—42no—
908C4—48no—
909C4—42no—
910C4—42no—
911C4—42no—
912C4—42no—
913C4—84no—
914C4—84no—
915C4—84no—
916C4#240618yes—
917C2—44no—
918C2—44no—
919C2—82no—
920C2C2×#240611yescharacteristic
921C2#3525011yescharacteristic
922C2#3530511yescharacteristic
923C2#3552112yes—
924C2#3727912yes—
925C2#3804012yes—
926C2#3804912yes—
927C2#3891512yes—
928C2#3892012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#2487C2semidirect
3. C2×#2486C2semidirect
4. C2×#2317C2semidirect
5. #16024C2semidirect
6. #15982C2semidirect
8. #15928C2semidirect
9. #15881C2semidirect
10. #15669C2semidirect
11. #15430C2semidirect
12. #15262C2semidirect
13. #15181C2semidirect
14. #15158C2semidirect
15. #14697C2semidirect
16. #14343C2semidirect
17. #14264C2semidirect
18. #13871C2semidirect
19. #13871C2semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#5292
C2×#24872
C2×#24862
C2×#23172
#160242
#159822
#159502
#159282
#158812
#156692
#154302
#152622
#151812
#151582
#146972
#143432
#142642
#138712